Question
Draw an angle of $45^\circ $, using a pair of compasses.
✓
Answer
Steps of constructions:
$1.$ Draw a ray $OA.$
$2.$ With centre $O$ and a suitable radius draw an arc meeting $O A$ at $E$.
$3.$ With centre E and with same radius, cut the first arc firstly at F and then from F with same radius cut act at $G .$
$4.$ With centres $F$ and $G$, with suitable radius, draw arcs intersecting each other at $H$.
$5.$ Join OH intersecting the first arc at $L$ and produce it to $C .$
$6.$ With centre $E$ and $L$ and with suitable radius draw arcs intersecting each other at $M$.
$7.$ Join $O M$ and produce it to $B$.
Then, $\angle\text{AOB}=45^\circ$
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